An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.

In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied.

In this paper, we investigate the reduced form of circulant matrices and we show that the problem of computing the q-th roots of a nonsingular circulant matrix A can be reduced to that of computing the q-th roots of two half size matrices B - C and B + C.

in this paper, some elementary operations on triangular fuzzynumbers (tfns) are defined. we also define some operations on triangularfuzzy matrices (tfms) such as trace and triangular fuzzy determinant(tfd). using elementary operations, some important properties of tfms arepresented. the concept of adjoints on tfm is discussed and some of theirproperties are. some special types of tfms (e.g. pu...

La division de la matrice est un geste relativement marginal en taille-douce. Que fragmentation du support vise recomposition ou déconstruction d’une plusieurs matrices préalablement gravées, cette pratique nous invite à repenser comme objet spécifiquement multiple.

Virtual rooms and common information spaces are being used more and more frequently. In addition to internet-based solutions, ad-hoc InfoSpaces have been proposed. Their security has not been sufficiently investigated. This paper proposes a new protocol for peer-to-peer data exchange with support for access control for operations in the virtual rooms. Access rights for operations are kept in ac...

In many problems of supervised tensor learning (STL), real world data such as face images or MRI scans are naturally represented as matrices, which are also called as second order tensors. Most existing classifiers based on tensor representation, such as support tensor machine (STM) need to solve iteratively which occupy much time and may suffer from local minima. In this paper, we present a ke...

The use of kernels is a key factor in the success of many classification algorithms by allowing nonlinear decision surfaces. Radial basis function (RBF) kernels are commonly used but often associated with dense Gram matrices. We consider a mathematical operator to sparsify any RBF kernel systematically, yielding a kernel with a compact support and sparse Gram matrix. Having many zero elements i...

We consider the problem of estimating the support of a vector β ∈ R based on observations contaminated by noise. A significant body of work has studied behavior of l1-relaxations when applied to measurement matrices drawn from standard dense ensembles (e.g., Gaussian, Bernoulli). In this paper, we analyze sparsified measurement ensembles, and consider the tradeoff between measurement sparsity, ...